Rate (M/N) code encoder, detector, and decoder for control data

ABSTRACT

A system for block encoding and block decoding of servo data with a rate (M/N) code, where M is an integer greater than 1 and N is an integer that is greater than M. Two codes are described for the encoding and decoding processes: a rate (2/6) code and a rate (2/8) code. In general, block encoding and block decoding maps between M servo data bits and N coded symbol bits. Such block encoding with a rate (M/N) code may be employed in a magnetic recording system for encoding servo data that is written to a servo data sector on a magnetic recording medium. Encoded servo data is read from the magnetic medium and block decoded. A forced maximum-likelihood, partial-response (PRML) detector is used to detect the N coded symbol bits from channel samples read from the magnetic medium. Block encoding provides greater coding gain for a detector when the characteristics of the block code are used to improve performance of the PRML detector that is used to detect the N coded symbol bits. Such PRML detector may employ a Viterbi algorithm (VA). State transition decisions over a block of N channel samples, or N clock cycles, form a path through a trellis of the VA, and the characteristics of the block code are used to force decisions for state transitions in the trellis. The PRML detector may force a decision for each state transition based on a priori knowledge of the known valid transitions defined by the rate (M/N) code symbol bits.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a continuation of copending application Ser. No. 09/413,082,filed on Oct. 6, 1999 U.S. Pat. No. 6,606,728, the teachings of whichare incorporated herein by reference; which copending application is acontinuation-in-part of application Ser. No. 09/338,104, filed on Jun.23, 1999, as attorney docket no. Aziz 4, now issued as U.S. Pat. No.6,480,984, the teachings of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to data encoding and data decodingemployed in transmission systems, and, more particularly, to a servoblock code for an encoder and a related trellis for a maximum-likelihooddetector used in conjunction with a decoder.

2. Description of the Related Art

Many digital transmission systems commonly employ maximum-likelihoodsequence detection to enhance detection of digital data represented by asequence of symbols (each symbol made up of a group of bits). The symbolbits are transferred as a signal through a transmission (communication)channel in which noise is typically added to the transmitted signal. Forexample, magnetic recording systems first encode data into symbol bitsthat are recorded on a magnetic medium. Writing data to, storing datain, and reading data from the magnetic medium may be considered atransmission channel that has an associated frequency response. A signalmay then be read from the magnetic medium as a sampled signal (i.e., asequence of output samples) representing the stored data (stored symbolbits). Magnetic recording systems for disk drives read and detect datafrom tracks on the magnetic medium (disk). Each track comprises user(“read”) data sectors as well as system dedicated control (e.g.,“servo”) data sectors embedded between read sectors. Servo data sectorsstore servo data that is a form of control data the recording systemuses 1) to search for tracks (during seek mode) and 2) to position aread head over the track on the magnetic medium. Some magnetic recordingsystems of the prior art employ digital signal processing to detect thestored servo data, while others may employ analog techniques.

FIG. 1 shows servo processing of a magnetic recording system 100. Aportion of the servo data is received by a servo data encoder 101 (shownas a 1/N encoder) that encodes the portion using a rate 1/N code that isdescribed subsequently. The remaining, non-encoded portion and encodedportion of the servo data are further processed by the magnetic writehead 102 and, then recorded on the magnetic is medium 110 A magneticread head 103 reads the information from the magnetic recording medium110 as an analog signal.

FIG. 2 shows a format for recording the servo data in the servo datasector of magnetic recording medium 110. Servo data may include apreamble 201 that is a sequence of bits from which timing and gaininformation is recovered. Timing and gain information allows themagnetic read head 103 to obtain gain and phase lock relative to theincoming analog signal provided from a track of the magnetic medium 110.Also shown in FIG. 2 is a burst demodulation field 204 that containsburst data. Burst data may be used by the magnetic read head 103 todetect whether the magnetic read head 103 is positioned directly overthe center of a track.

The preamble 201 may be followed by an encoded servo address mark (SAM)202, which in turn may be followed by encoded Gray data 203 for theservo sector. The SAM 202 comprises a predetermined bit pattern toidentify the sector as containing servo data, and may be employed toreset a framing clock used by the magnetic read head 103 to readtracks/sectors from the magnetic recording medium 110. The Gray data 203represents the track number and cylinder information of the magneticrecording medium, and may be used by the magnetic read head 103 to avoiderrors when reading adjacent tracks during seek mode. The SAM 202 andGray data 203 are usually the portions of the servo data that areencoded as sequences of symbol bits before being recorded, on themagnetic recording medium 110.

Returning to FIG. 1, magnetic read head 103 may provide a sampled analogsignal representing the recorded and encoded servo data as outputchannel samples. The term “output channel sample” indicates that thedata has passed through a transmission channel (e.g., magnetic medium110) that has a form of frequency response (possibly having memory).This type of transmission channel (possibly including a frequencyresponse of a subsequent equalizer) may be termed a partial responsechannel. The signal representing the encoded servo data has an addednoise component and added signal distortion caused by passing the signalthrough the channel's frequency response. To partially correct forvariations in the channel's frequency response or for frequency responsecharacteristics of the circuitry of magnetic read head 103, the outputchannel samples may be applied to equalizer 104. The equalized outputchannel samples are then applied to a partial-response,maximum-likelihood (PRML) detector 105.

The PRML detector 105 employs an algorithm, such as the Viterbialgorithm (VA), to detect the sequence of symbol bits representing, forexample, the encoded SAM 202 and encoded Gray data 203 from the outputchannel samples. Servo data decoder 106 (shown as a 1/N decoder)receives the detected symbol sequence from PRML detector 105 and decodesthe sequence of symbol bits to reconstruct the servo data. Also shown isthe burst demodulator 107, which extracts the burst demodulation datafrom the equalized output channel samples provided by equalizer 104.

Both the SAM 202 and Gray data 203 are encoded by the servo data encoder101 by mapping each input bit to N output symbol bits, giving a codingrate of (1/N). For example, the biphase code of the prior art maps a “1”to a “1100” sequence, and a “0” to a “0011” sequence. Such biphase codehas a rate (1/4), and such biphase code is described in, for example,U.S. Pat. No. 5,661,760. As the coding rate (1/N) approaches unity, lessredundancy, and so less format overhead, is introduced by the encodingprocess when recording the servo data.

The Viterbi algorithm (VA) employed by PRML detector 105 provides amaximum a posteriori estimate of a state sequence of a finite-state,discrete-time Markov process observed in noise. Given a receivedsequence of channel output samples of a signal corrupted with additivenoise, the VA finds a sequence of symbol bits which is “closest” to thereceived sequence of channel output samples. For the VA, closest isrelative to a predefined metric. As is known, in a communication channelwith additive white gaussian noise (AWGN), the VA may be the optimal,maximum-likelihood sequence-detection algorithm. The VA forms a trelliscorresponding to possible states (portion of received symbol bits in thesequence) for each received output channel symbol per unit increment intime (i.e., clock cycle). Transitions between states in the trellis areusually represented by a trellis diagram in which the number of bits(corresponding to output channel samples and detected symbol bits) for astate is equivalent to the memory of the partial response channel.Transitions are “weighted” according to the predefined metric, andEuclidean distance may be used as a metric for the trellis structure.

FIG. 3 shows an 8-state trellis employed for a partial response channelhaving a memory length of three (e.g., an EPR4 channel with response1+D−D²−D³). The left column 301 of 3-bit states d(n−3,j), d(n−2,j),d(n−1,j) represents state symbol bits for the channel samples in thePRML detector 105 during a previous clock cycle, while the right column302 of 3-bit states d(n−2,k), d(n−1,k), d(n,k) represents state symbolbits for the channel samples during the current clock cycle. For thisnotation, in “d(n−1,j)”, the j is the state in the trellis at time (n−1)(i.e., one of the states of the left column 301) and in “d(n,k)”, k isthe state at time n i.e., (i.e., one of the states of the left column302). The right column 302 includes the state symbol bit, d(n,k) thatcorresponds to the currently received output channel sample at time n.

Each line, termed a branch, connecting the states in the left and rightcolumns 301 and 302 represents a transition from a previous state of thetrellis (i.e., a state of the previous trellis phase) to a current statethe trellis (i.e., a state of a current trellis phase). The branch is aportion of a possible path through the trellis, and may be included inmore than one path. For example, a branch connects the state #0 (“000”)in the left column 301 (the originating state) to state #0 (“000”) inthe right column 302. This branch represents a potential decision of thedetector that not only identifies the current channel sample d(n,0) asbeing a “0” symbol, but also for the path representing the sequence ofsymbol bits received by the PRML detector 105 up to time n. A branchalso connects the state #4 (“100”) to state #0 (“000”) and represents apotential decision for channel sample d(n,0) being a “0” symbol exceptthat now the originating state is “100”. Therefore, two paths branchesfrom the previous state may pass through the present state “000”.

Similarly, two branches pass through each of the other states in thecurrent trellis phase. Any destination state k ending in a “0”represents d(n,k) being the “0” symbol for the path going through statek while any destination state k ending in a “1” represents d(n,k)equivalent to the “1” symbol for the path going through state k. Ingeneral, the different possible paths may be represented by a P-statetrellis where P=2^(Q), Q an integer equivalent to the state length(i.e., memory length of the partial response channel). An EPR4 channelhas the response 1+D−D²−D³ and has 3-bit states, requiring a 2³=8-statetrellis. The EEPR4 channel has the response 1+2D−2D³−D⁴ and has 4-bitstates, requiring a 2⁴=16-state trellis.

The VA recursively performs three steps to detect a path through atrellis corresponding to the received sequence of symbol bits. First,branch metrics for the trellis are calculated for the current states;second, updates for each state metric (sm, which is defined below) arecalculated for all states; and, third, survivor paths are determined.The survivor path represents the sequence of symbol bits entering agiven state which is closest, according to the Euclidean distance, tothe received sequence of symbol bits in noise. The branch metric for astate transition is defined as the Euclidean distance between thereceived output channel sample (yr[n]) and the ideal channel outputsample (yi[n]) corresponding to the transition. To compute the entire,or global, sequence most likely received, the VA recursively calculatesand updates state metrics of all states to provide a minimum path metricover several state transitions.

For the VA described above, the branch metric bm (Euclidean distance) ofa given transition is defined as the negative logarithm of thelikelihood function with respect to the received noisy output channelsample yr[n] and the ideal output channel sample yi[n]. Therefore, thebranch metric bm (j,k,n) for the transition from the jth state at timen−1 to the kth state at time n, for the exemplary VA algorithm, is givenby equation (1):

bm(j,k,n)=−ln ƒ(yr[n]−yi[n])  (1)

where yi[*] is the ideal channel output sample corresponding to thetransition from the jth state to the kth state, and ƒ(*) is theprobability density function of the Gaussian noise sequence.

For each state, an add-compare-select (ACS) operation determines theminimum state metric sm for the state based on the previously calculatedstate metrics of two originating states j and b as well as the branchmetrics of the two branches of these states arriving at the currentstate k. The ACS operation thus determines the state metric sm of statek at time n and can be described by equation (2)

sm(k,n)=min((sm(j,n−1)+bm(j,k,n)), (sm(b,n−1)+bm(b,k,n)))  (2)

where j and b are the two possible originating states, sm(j,n−1) andsm(b,n−1) are the state metrics of the originating states at theprevious time (n−1), bm(j,k,n) represents the branch metric of thebranch connecting states j and k at time n, and bm(b,k,n) represents thebranch metric of the branch connecting states b and k at time n.

The VA finds the maximum likelihood sequence by determining the sequenceof symbol bits, or path, through the trellis that provides a minimumpath metric. The path metric is simply the accumulated branch metrics ofdifferent branches encountered by the path through phases of the trellisas different possible paths are considered. The state metric of a givenstate is the path metric at some particular time if the path includesthe given state at that particular time.

A prior art implementation of the ACS operation for a pair of paths(branches) (termed an ACS unit) is shown in FIG. 4. Adders 404 and 405each provide the sum of the state metric of time n−1 and branch metricof time n for a different path (termed a path sum). The comparator 401compares the path sums provided by adders 404 and 405 and provides anoutput signal indicating which path sum has a minimum value. Multiplexer(MUX) 402, based on the output signal of the comparator 401, selects asthe state metric sm for the current clock cycle (time n) the path sumhaving the minimum value.

Each branch corresponds to one decision for a symbol d(n,k), whichsymbol is either a “0” for one branch and a “1” for the other branch.The decision for selecting one branch over the other branch alsocorresponds to the decision for the value of ideal output channel sampleyi[n]. At time n, the ideal output channel sample is either yi[j,k,n] oryi[b,k,n], where yi[j,k,n] is the ideal output channel sample yi[n]going from state j to state k. The branch metrics are calculated as inequation (1) (i.e., bm(j,k,n)=(yr[n]−yi[j,k,n])² andbm(b,k,n)=(yr[n]−yi[b,k,n])² where yr[n] is the received output channelsample at time n). MUX 403, also based on the output signal of thecomparator 401, selects either a “0” or “1” (corresponding to the symbolvalue of a branch) as a tentative decision made for the current symbold(n,k). Therefore, for each state, the comparator 401 selects theminimum state metric for the current clock cycle and also provides atentative decision for the current data bit d(n,k) in a path memory forstorage and shifting.

The operation of the detector (i.e., the transition between states ofthe trellis) is described with respect to FIGS. 3 and 4 for a singleclock cycle. For several clock cycles, the trellis is extended byrepeating the basic trellis shown in FIG. 3. Each state in a trellisphase has a corresponding ACS unit. During each clock cycle, thecombined ACS units for the corresponding states in the trellis phaseshift P=2^(Q) bits, (i.e., d(n,k), (k=0, . . . , P−1), into the pathmemory. After some decision delay, the PRML detector 105 forms a finaldecision as to which one of possible paths through this memory has aminimum path metric, and so corresponds to the most likely sequence ofreceived symbol bits.

SUMMARY OF THE INVENTION

The present invention relates to circuits and methods for a system thatencodes, records, detects, and decodes control data stored on a medium.The control data is encoded and decoded based on aerate M/N code thatmaps between a block of M data bits of the control data and a block of Nsymbol bits. The block of N symbol bits form a symbol representing theblock of control data, where M is an integer greater than 1 and N is aninteger greater than M. The control data may be used for subsequentlyreading information from the medium after recording. In accordance withan embodiment of the present invention, encoding comprises mapping ablock of M bits of a sequence of control data into a block of N symbolbits and storing the N symbol bits on the medium.

In accordance with an exemplary embodiment, a sequence of blocks of Nsymbol bits is generated from a sequence of channel samples read from amedium and representing information. For this further embodiment,successive portions of the sequence of channel samples are received astransitions between sequential states of a trellis, wherein the sequenceof channel samples corresponds to the sequence of blocks of N symbolbits. A set of trellis phases and a set of forcing phases aresynchronized to the sequential states, the set of trellis phasescorresponding to a block of N channel samples. A path through states ofthe set of trellis phases is determined in accordance with amaximum-likelihood detection algorithm. The path of states correspondsto a received block of N symbol bits, and wherein, for each trellisphase, a corresponding forcing phase provides, if necessary, a forceddecision to the maximum-likelihood detection algorithm for a transitionbetween states in the trellis, the forced decision based on a constraintof the rate (M/N) code.

In accordance with another exemplary embodiment, a sequence of symbolbits is generated from a sequence of channel samples read from a medium,the symbol bits representing a sequence of control data to be used forsubsequently reading information from the medium. Blocks of N symbolbits are received, with each block of N symbol bits formed based on arate (M/N) code applied to a block of M bits of control data. Each blockof N symbol bits is mapped into a block of M bits based on the rate(M/N) code to generate the sequence of control data.

BRIEF DESCRIPTION OF THE DRAWINGS

Other aspects, features, and advantages of the present invention willbecome more fully apparent from the following detailed description, theappended claims, and the accompanying drawings in which:

FIG. 1 shows servo processing of a magnetic recording system of theprior art;

FIG. 2 shows a format for servo data recorded in the servo data sectorof a magnetic recording medium for the system of FIG. 1;

FIG. 3 shows an 8-state trellis of a Viterbi algorithm and employed by aPRML detector for a partial response channel having a memory length ofthree;

FIG. 4 shows a prior art implementation of an add-compare-selectoperation of the Viterbi algorithm of FIG. 3 for a pair of paths in atrellis;

FIG. 5 shows an exemplary servo data recording system in accordance withthe present invention;

FIG. 6a shows an exemplary implementation of an encoding circuit for theservo data block encoder of FIG. 5 that employs a rate (2/6) code;

FIG. 6b shows an exemplary implementation of a decoding circuit for theservo data block decoder of FIG. 5 that employs a rate (2/6) code;

FIG. 7 shows a 16-state trellis used with the Viterbi algorithm for anexemplary rate (2/6) code of the present invention passing through apartial response channel having a memory length of four;

FIG. 8 shows remaining valid transitions between states of the trellisof FIG. 7 that satisfy constraints of the exemplary rate (2/6) code;

FIG. 9 shows a resulting trellis when the trellis of FIG. 7 is prunedbased on the valid state transitions shown in FIG. 8;

FIG. 10 shows a resulting trellis over 12 clock cycles when the trellisof FIG. 9 is pruned to remove illegal paths;

FIG. 11 shows an exemplary embodiment of an ACS circuit for the forcedPRML detector of FIG. 5 implementing a pruned trellis in accordance withthe present invention;

FIG. 12 shows the valid transitions between states in an 8-state trellisthat satisfy constraints of the exemplary rate (2/6) code for a channelhaving a memory length of three;

FIG. 13 shows a pruned trellis that accounts for the valid transitionsshown in FIG. 12;

FIG. 14 shows the valid transitions between states in an 8-state trellisthat satisfy constraints of the exemplary rate (2/8) code for a channelhaving a memory length of three;

FIG. 15 shows a pruned trellis that accounts for the valid transitionsshown in FIG. 14;

FIG. 16 shows the valid transitions between states in an 16-statetrellis that satisfy constraints of the exemplary rate (2/8) code for achannel having a memory length of four; and

FIG. 17 shows a pruned trellis that accounts for the valid transitionsshown in FIG. 16.

DETAILED DESCRIPTION

In accordance with exemplary embodiments of the present invention, servodata is block encoded with a rate (M/N) code, where M is an integergreater than 1 and N is an integer greater than M. In the describedembodiments, servo data is block encoded or block decoded (i.e., thecode is a mapping between M bits and a group of N symbol bits. For thepreferred embodiments described herein, two codes are described for theencoding and decoding processes: a rate (2/6) code and a rate (2/8)code. Encoding in accordance with the present invention may providegreater coding gain for a detector due to the characteristics of blockencoding with the rate (M/N) code. In accordance with some exemplaryembodiments of the present invention, a forced, maximum-likelihood,partial-response (PRML) detector, such as a detector employing theViterbi algorithm, may employ the characteristics of the block code toforce decisions for detected encoded servo data values. The forced PRMLdetector may force a decision for each state transition between statescorresponding to output channel samples received from a transmissionchannel, the output channel samples representing servo data encoded inaccordance with the rate M/N code of the present invention.

The exemplary embodiments of the present invention are described hereinas employed in a magnetic recording system for encoding and decodingservo data of a servo data sector. As would be apparent to one skilledin the art, the techniques as described herein may be extended toencoding and decoding in other types of data transmission systems inwhich PRML detectors are used, such as optical recording systems. Inaddition, the present invention may in general be extended to encodingand decoding processes employing codes of differing rates, and so thepresent invention is not limited to the two codes described herein.

FIG. 5 shows an exemplary servo data recording system 500 in accordancewith the present invention. Servo data recording system 500 comprises aservo data block encoder 501, optional equalizer 503, forced PRMLdetector 504, forcing logic 506, and servo data block decoder 505.Encoded servo data is generally passed through a transmission channel502 with encoded user data, system timing and gain information, andother peripheral information used by the system 500.

Transmission channel 502 includes a medium, such as magnetic medium oroptical disk, that information is recorded on. Servo data recordingsystem 500 receives control data that is employed by the system 500 toenable the system 500 to read information from the medium. The controldata is also stored on the medium of the transmission channel 502. Forthe exemplary embodiments described herein, the control data is servodata employed by the servo of a magnetic read head to seek and locatetracks/sectors and position the servo over tracks/sectors on the medium.As would be apparent to one skilled in the art, the present invention isnot so limited to servo data of magnetic recording systems, but may beemployed for control data of other systems. Such systems may be opticalsystems that employ control data to control analogous functions of thelaser-based read operation of the optical disk.

Servo data recording system 500 receives a sequence of servo datawordsthat include servo data that is to be encoded and may include servo datathat is recorded directly on the magnetic medium. Servo data blockencoder 501 (shown as a (M/N) block encoder) receives a sequence ofdatawords a that are to be encoded, each dataword a being of length M.The sequence of datawords represents the servo data to be encoded (e.g.,Servo Address Mark (SAM) and Gray data). Servo data block encoder 501applies a rate (M/N) block code to each dataword a to form acorresponding codeword z of length N. This block encoding process formsblocks of symbol bits defined by block boundaries. The sequence ofcodewords z is then transmitted as a signal through transmission channel502, such as a magnetic recording channel or an optical recordingchannel. The transmission channel 502 and equalizer 503 have a partial(frequency) response with memory, and may be, for example, an EPR4 orEEPR4 channel of a magnetic recording medium. In addition to thecharacteristics of the recording medium, transmission channel 502 mayalso represent the combined frequency characteristics of the preceding,write and read head transfer functions, signal equalization, andfiltering processes that are applied to the analog signal representingthe sequence of codewords z.

After passing through the transmission channel 502, the signalrepresenting the sequence of transmitted codewords z is then read fromthe transmission channel 502 and provided as a sequence of outputchannel samples. The sequence of output channel samples may be equalizedby the optional equalizer 503 to provide the samples yr. Optionalequalizer 503 corrects for variations in the characteristics of therecording channel or other device frequency characteristics specific tothe implementation of system 500 that the signal passes through.

The sequence of equalized output channel samples yr is applied to aforced, partial-response-maximum likelihood (PRML) detector 504 thatdetects each codeword z from the sequence of output channel samples yr.Forced PRML detector 504 may employ a Viterbi algorithm (VA). Forcinglogic 506 also receives the sequence of output channel samples yr;detects a beginning of the encoded servo data; synchronizes the VA tothe block encoding process; and generates a forcing signal FS. Forcingsignal FS is generated based on the constraints of the rate (M/N) codeand the trellis phase of the VA synchronized to the block encodingprocess. Forced PRML detector 504 may employ the forcing signal FS toforce decisions for symbol bits of codeword z corresponding to thecurrent detected output channel sample by, for example, pruning thetrellis of the VA employed by the forced PRML detector 504. The methodof pruning of the VA the trellis is described subsequently.

Rate (M/N) Code

An encoder, such as servo data block encoder 501 of FIG. 5, maps aninput dataword a to an output codeword z. Defining the input dataword aof M bits as elements a(1), a(2), . . . , a(M), a set of logic equationsmay be derived that map the input dataword a to an output codeword z ofN symbol bits defined as elements z(1), z(2), . . . , z(N). For example,the rate (2/6) code maps from a=“00” to z=“000111”, a=“11” toz=“111000”, a=“01” to z=“110011” and a=“10” to z=“001100”. This mappingmay be implemented with registers and combinational logic circuits thatoperate in accordance with the logic equations. Table 1 provides logicequations for exemplary mappings that may be implemented for the rate(2/6) code and rate (2/8) code, where a “!” represents a logicalcomplement operation.

TABLE 1 Rate (2/6) Code Rate (2/8) Code Decoder Decoder EncoderEquations Equations Encoder Equations Equations z(1) = a(2) x(1) = z(3)z(1) = a(1) x(1) = z(1) z(2) = a(2) x(2) = z(1) z(2) = a(1) x(2) = z(5)z(3) = a(1) z(3) = !a(1) z(4) = !a(2) z(4) = !a(1) z(5) = !a(1) z(5) =a(2) z(6) = !a(1) z(6) = a(2) z(7) = !a(2) z(8) = !a(2)

An encoding circuit as shown in FIG. 6a may be employed to implement theencoding logic equations given in Table 1 for the rate (2/6) code.Elements a(1) and a(2) of the dataword a are received serially by a2-bit register 601. The elements a(1) and a(2) may be provided inparallel from 2-bit register 601 in accordance with a dataword clock.The complements of a(1) and a(2) are provided from inverters 604 and603, respectively. The elements a(1), !a(1), a(2) and !a(2) are providedin parallel to corresponding stages of 6-bit register 602. The contentsof 6-bit register 602 correspond to the elements z(1), z(2), z(3), z(4),z(5), and z(6). Elements z(1), z(2), z(3), z(4), z(5), and z(6) may beserially provided from 6-bit register 602 in accordance with a codewordclock to provide the output codeword z.

A decoder, such as the servo data block decoder 505 of FIG. 5, mapselements of the codeword z to elements of a decoded dataword x havingelements x(1) through x(M). The elements of x desirably correspond tothe elements of a, but may contain errors introduced by, for example,noise in a transmission channel. In a similar manner to the encoder, aset of logic equations may be employed to represent this mapping by thedecoder. For the exemplary rate (2/6) rate code, the elements z(1)through z(6) of codeword z map logically to elements x(1) and x(2) ofdecoded dataword x as given in Table 1 above. A decoding circuit asshown in FIG. 6b may be employed to implement the decoding logicequations given in Table 1 for the rate (2/6) code. The decoding circuitincludes a 6-bit register 605 and 2-bit register 606. The input codewordz is received serially into 6-bit register 605 in accordance with acodeword clock and selected elements loaded in parallel intocorresponding stages of 2-bit register 606. The contents of 2-bitregister 606 are provided serially in accordance with a dataword clockas elements x(1) and x(2) (corresponding to the elements a(1) and a(2)).Since the decoded dataword elements x(1) and x(2) are duplicated amongthe elements of codeword z, for some embodiments additional circuitry(not shown) may implement a “voting” method prevent selecting elementsof z that have bit-errors as elements x(1) and x(2).

Also shown in Table 1 are the logic equations for encoding and decodingin accordance with the rate (2/8) code. The rate (2/8) code maps inputdatawords a of “00”, “11”, “01”, and “10” to output codewords z of“00110011”, “11001100”, “00111100”, and “11000011”, respectively. Therate (2/8) code mapping may be implemented with an encoding circuit anda decoding circuit analogous to those shown in FIGS. 6a and 6 b.

For an encoder, the mapping of the dataword a to codeword z is notunique and, as would be evident to one skilled in the art, may berearranged to achieve a different mapping having a different performance(as measured by, for example, coding gain). For example, the rate (2/6)code could map a=“00” to z=“110011” instead of z=“000111”. Similarly,for a decoder, the mapping from the codeword z to decoded dataword x isnot unique. For a decoder in accordance with the exemplary rate (2/6)code, the element x(1) may also be obtained as x(1)=!z(5) or x(1)=!z(6).Similarly, element x(2) may also be obtained as x(2)=z(2) or x(2)=!z(4).As with the rate (2/6) code, the logic equations for the rate (2/8) codeencoder and decoder are not unique.

PRML Detection and Forcing Trellis Decisions

For the exemplary embodiments of the present invention, the servo datablock encoder 501 encodes and servo data block decoder 505 decodes inaccordance with a rate (2/6) code or a rate (2/8) code. In general, therate (M/N) code is a constrained code because not all possiblebit/symbol patterns occur or are defined, and specific bit/symbolpatterns arise across block boundaries. In FIG. 5, the encoded servodata (SAM and Gray data) are detected by means of a forced,partial-response, maximum-likelihood (PRML) detector 505 that mayimplement steps of a program that employs a Viterbi algorithm (VA). Theforced PRML detector 505 may typically be implemented with a processor,memory, and a plurality of Add-Compare-Select circuits. The processor ofthe forced PRML detector 505 may use knowledge of constraints imposed bythe rate (M/N) block code process to reduce the probability of falsedetection. The probability of false detection refers to the actual orfinal decision of a state of a current trellis phase of the VA notcorresponding to the actual value represented by the current outputchannel sample yr[n].

For a constrained code, the trellis employed in the forced PRML detector504 is pruned by forcing the VA to select only certain branches in thetrellis. The process of forcing uses constraints imposed by the blockcode to select branches corresponding only to valid state transitions.In general, for a code of block size B, the set of valid transitionsconstrained by the code will be different in the trellis over B clockcycles, corresponding to B forcing phases, and then the set repeatsevery B clock cycles.

FIG. 7 shows a 16-state trellis of the VA for the rate (2/6) code ofTable 1. The 16-state trellis may be employed when output channelsamples provided to the forced PRML detector 504 (FIG. 5) are read froma magnetic medium that has an EEPR4 channel response. In FIG. 7, theinitial input to the detector are decisions d(n−4), d(n−3), d(n−2),d(n−1) related to the values of the four channel samples yr[n−4] throughyr[n−1]). At time n−1 (i.e., the previous clock cycle) the correspondingstate in column 703 of the trellis is one of 16 possible states: state#0 (“0000”), corresponding to d(n−4)=0, d(n−3)=0, d(n−2)=0, d(n−1)=0,through state #15 (“1111”), corresponding to d(n−4)=1, d(n−3)=1,d(n−2)=1, d(n−1)=1. If the trellis phases are synchronized to the blockencoding that is described subsequently, then yr[n−4] through yr[n−1]correspond to the last four symbol bits of the previous block of symbolbits.

At time n a new output channel sample yr[n] is added and the next statein column 706 of the trellis is again one of 16 possible states (state#0 (“0000”), corresponding to d(n−3)=0, d(n−2)=0, d(n−1)=0, d(n)=0,through state #15 (“1111”) corresponding to d(n−3)=1, d(n−2)=1,d(n−1)=1, d(n)=1). The new output channel sample yr[n] corresponds tothe first symbol bit of the current block to be decoded. The next statein column 706 corresponds to the first phase of the current trellis.

The rate (2/6) code maps from “00” to “000111”, “11” to “111000”, “01”to “110011” and “10” to “001100”. The mapping constrains the sequence ofsymbol bits such that only certain groups of symbol bits appear. Aconstraint of the rate (2/6) code is, for example, that the last foursymbol bits of a block adjacent to the first symbol of the next blockmay only be “0011”, “1000”, “0111”, and “1100”. Consequently, thetransition from state #0 of column 703 (i.e., “0000”) to any state ofcolumn 706 in the current trellis in FIG. 7 is an “illegal” transitionbecause the last four symbol bits of a previous block cannot be “0000”.Therefore, these branches from state “0000” in column 703 may beeliminated. This process may be repeated to identify all validtransitions based on the rate (M/N) code constraints. The constraintsforce the valid transitions upon the 16-state trellis for each of sixforcing phases of the trellis (FP=1 to 6). FIG. 8 shows the validtransitions that satisfy constraints of the exemplary rate (2/6) code(16-state trellis). For example, the column 803 of the previous trellisonly includes state #3 (“0011”), state #7 (“0111”), state #8 (“1000”),and state #12 (“1100”). The valid transitions (branches) in FIG. 8 areshown as dashed lines.

FIG. 9 shows pruning of the trellis given in FIG. 7 based on the validtransitions shown in FIG. 8. The following four steps generate thepruned trellis of FIG. 9 as follows. First, all possible transitions ina trellis phase of FIG. 7 are considered. Second, valid transitions ofthe corresponding trellis phase in FIG. 8 required by the code areidentified with dashed lines. Third, identify each original transitionof FIG. 7 (a branch indicated as a solid line) that arrives at a statein the next phase that is also reached as a transition indicated with adashed line of FIG. 8. Fourth, delete the branches corresponding to thesolid-line transition identified in the third step to give preference tothe dashed lined transition desired by the code.

In FIG. 9, some states have no branches leave the state during someforcing phases and no pruning occurs during forcing phases FP=2 andFP=4. However, the trellis of FIG. 9 still allows “illegal” paths topropagate through the trellis (i.e., a path may be followed through thetrellis consisting of only solid lines). To block illegal states, thetrellis of FIG. 9 is pruned further. FIG. 10 shows the result of suchpruning of FIG. 9, and FIG. 10 also shows the pruned (valid) statetransitions over 12 clock cycles (two blocks of symbol bits). Thetrellis of FIG. 10 illustrates that illegal paths may be blocked:tracing a path through the trellis comprising only solid lineseventually leads to an end state which is eliminated in one of theforcing phases (no branches leave the end state).

For FIG. 10, the additional pruning of the trellis of FIG. 9 occursduring FP=5, where branches leaving state #4 through state #11 aredeleted. The trellises of FIG. 8 and FIG. 9 are specified by the code,but the trellis of FIG. 10 is not necessarily unique. Alternativeembodiments including different pruning (in addition to the pruning ofthe code constraints) may equivalently stop illegal paths. However,among these alternative embodiments, some trellises may be preferredbased on detector performance, given limitations in fixed-pointcomputation of particular implementations and finite decision delay inthe path memory of, for example, the forced PRML detector 504 (FIG. 5).

The preference for selecting one branch over another branch is forcedby, for example, the forcing signal FS applied forced PRML detector 504of FIG. 5. The forcing signal has a component FS, for each state of atrellis phase, and each state of a trellis phase has a correspondingadd-compare-select (ACS) operation performed by an ACS circuit. Forexample, a 16-state trellis may require 16 ACS circuits. Each componentFS_(i) is generated by peripheral forcing phase digital controlcircuitry, such as the forcing logic 506 of FIG. 5. The forcing signalcomponent FS_(i) for the ith state is applied to the ACS circuitcorresponding to state i. Forcing signal component FS_(i) selects one ofthe two incoming branches to a state during the select portion of theACS operation. An exemplary embodiment of an ACS circuit in accordancewith the present invention as may be employed in the forced PRMLdetector 504 of FIG. 5 is shown in FIG. 11.

FIG. 11 shows adders 1101 and 1102 each provide a sum of the statemetric and branch metric of time n−1 for a respective path (path sum).Comparator 1103 compares the path sums provided by adders 1101 and 1102to provide an output signal indicating which path sum has a minimumvalue. The select operation of each of the MUXs 1104 and 1105 is nowdetermined not only based on the output signal of comparator 1103, butalso based on the forcing signal component FS_(i) for the correspondingforcing phase of the pruned trellis. When the forcing signal componentFS_(i) indicates that no forcing is warranted, MUX 1104 selects as thestate metric sm for the current clock cycle the path sum having theminimum value. When the forcing signal component FS_(i) indicates thatforcing is warranted, MUX 1104 selects as the state metric sm for thecurrent clock cycle the path sum corresponding to the valid transitionbranch of the pruned trellis.

As described before, each branch corresponds to one decision d(n,k) fora symbol bit, and also corresponds to an ideal output channel sampleyi[n]. At time n, the ideal output channel sample is yi(j,k,n) oryi(b,k,n). The branch metrics are calculated as given in equation (1),i.e., bm(j,k,n)=(yr[n]−yi[j,k,n])² and bm(b,k,n)=(yr[n]−yi[b,k,n])²where yr[n] is the received output channel sample at time n. MUX 1105,also based on the output signal of the comparator 1103 and the forcingsignal component FS_(i), selects either a “0” or “1” as a tentativedecision made for the current symbol d(n,k). MUX 1105 selects thedesired symbol on the select signal since a particular path (statetransition) always corresponds to either a “0” or a “1” decision.Therefore, for each state transition, the minimum state metric for thecurrent clock cycle is selected and a tentative decision for the currentdata bit d(n,k) is provided to a path memory for storage and shifting.

The operation of a forcing signal for each of the forcing phases (FPs)embodied in the pruned trellis of FIG. 10 may be described as follows

FOR FP=1 to 6:

If FP=1

Force state #0 to come from state #8

Force state #1 to come from state #8

Force state #6 to come from state #3

Force state #7 to come from state #3

Force state #8 to come from state #12

Force state #9 to come from state #12

Force state #14 to come from state #7

Force state #15 to come from state #7

If FP=2

No forcing

If FP=3

Force state #0 to come from state #0

Force state #1 to come from state #0

Force state #6 to come from state #3

Force state #7 to come from state #3

Force state #8 to come from state #12

Force state #9 to come from state #12

Force state #14 to come from state #15

Force state #15 to come from state #15

If FP=4

No forcing

If FP=5

Force state #0 to come from state #0

Force state #1 to come from state #0

Force state #2 to come from state #1

Force state #3 to come from state #1

Force state #4 to come from state #2

Force state #5 to come from state #2

Force state #6 to come from state #3

Force state #7 to come from state #3

Force state #8 to come from state #12

Force state #9 to come from state #12

Force state #10 to come from state #13

Force state #11 to come from state #13

Force state #12 to come from state #14

Force state #13 to come from state #14

Force state #14 to come from state #15

Force state #15 to come from state #15

If FP=6

Force state #3 to come from state #9

Force state #7 to come from state #3

Force state #8 to come from state #12

Force state #12 to come from state #6

The forced PRML detector 504 preferably synchronizes the states of thetrellis of the VA to the block encoding process. Consequently, therelationship between 1) block boundaries of the encoded servo data and2) the forcing phase sequence is determined before the sequencedetection begins. The forced PRML detector 504 is forced oncesynchronization occurs. Synchronization may employ a small number of padbits inserted after the preamble of the servo data, allowing fordetection of the end of the preamble. The preamble may not necessarilybe encoded with the rate (M/N) code, but a pad bit may be addedrepresented by a rate (M/N) code symbol. The end of the preamble may bedetected by filtering a copy of the received channel output samples andapplying the filtered channel output samples to a threshold detector.Pad bits for the rate (2/6) and rate (2/8) codes are preferably insertedbetween the preamble and SAM.

FIGS. 12 through 17 show pruned trellis transitions for the rate (2/6)code (8-state trellis) and rate (2/8) code (8- and 16-state trellises)of Table 1. FIG. 12 shows the valid transitions imposed by the rate(2/6) code (8-state trellis), and FIG. 13 shows the forced or prunedtrellis taking into account the valid transitions of FIG. 12. FIG. 14shows the valid transitions imposed by the rate (2/8) code (8-statetrellis), and FIG. 15 shows the forced or pruned trellis taking intoaccount the valid transitions of FIG. 14. FIG. 16 shows the validtransitions imposed by the rate (2/8) code (16-state trellis), and FIG.17 shows the forced or pruned trellis taking into account the validtransitions of FIG. 16. For each of the rate (2/6) code (8-statetrellis), rate (2/8) code (8-state trellis), and rate (2/8) code(16-state trellis) a final, pruned trellis maybe generated as describedabove with regard to the rate (2/6) code, 16-state pruned trellisstructure. The final, pruned trellis has illegal paths eliminated byselecting appropriate forcing phases that eliminate a large number ofstates through which paths with solid lines pass.

Coding Gain

The relative performance of different rate codes may be compared using ameasure of the detection reliability bit-error rate. Such measure may bea ratio of 1) the minimum distance obtained in a system employing aparticular rate code (dmc) and 2) the minimum distance obtained in asystem employing no code (dmu). The quantity known in the art as thecoding gain may be defined as 20 log (dmc/dmu) dB. The minimum distancemay be the minimum Euclidean distance between two error events that maybe falsely identified (i.e., the distance between the two error eventsthat are the most likely to be confused with one another). Coding gainfor a particular rate code employed to encode servo data is dependentupon the partial response of the channel. Table 2 summarizes exemplarycoding gains of the rate (2/6) code and rate (2/8) code and the biphasecode of the prior art. Table 2 also summarizes exemplary coding gainsfor a rate (3/8) code in accordance with the present invention. The rate(3/8) code may be formed based on the rate (2/8) code.

TABLE 2 Coding Gain (dB) Code Code Symbol bits Rate EPR4 channel EEPR4channel Biphase 1 = 1100; 0=0011 1/4 8.45 8.57 2/6 11 = 111000 1/3 6.997.32 00=000111 10=001100 01=110011 2/8 00=00110011 1/4 8.45 8.5711=11001100 01=00111100 10=11000011 3/8 000=00110011 3/8 4.77 6.02111=11001100 001=00111100 110=11000011 010=11111111 101=00000000100=11110000 011=00001111

The calculated coding gains in Table 2 are for both the EPR4 magneticrecording channel (i.e., 8-state trellis for VA) and EEPR4 magneticrecording channel (i.e., 16-state trellis for VA).

While the exemplary embodiments of the present invention have beendescribed with respect to methods for encoding and decoding, the presentinvention is not so limited. As would be apparent to one skilled in theart, various methods may be implemented as functions of circuit elementsand may also be implemented in the digital domain as processing steps ina software program. Such software may be employed in, for example, adigital signal processor, micro-controller or general purpose computer.

The present invention can be embodied in the form of methods andapparatuses for practicing those methods. The present invention can alsobe embodied in the form of program code embodied in tangible medium,such as floppy diskettes, CD-ROMs, hard drives, or any othermachine-readable storage medium, wherein, when the program code isloaded into and executed by a machine, such as a computer, the machinebecomes an apparatus for practicing the invention. The present inventioncan also be embodied in the form of program code, for example, whetherstored in a storage medium, loaded into and/or executed by a machine, ortransmitted over some transmission medium, such as over electricalwiring or cabling, through fiber optics, or via electromagneticradiation, wherein, when the program code is loaded into and executed bya machine, such as a computer, the machine becomes an apparatus forpracticing the invention. When implemented on a general-purposeprocessor, the program code segments combine with the processor toprovide a unique device that operates analogously to specific logiccircuits.

It will be further understood that various changes in the details,materials, and arrangements of the parts which have been described andillustrated in order to explain the nature of this invention may be madeby those skilled in the art without departing from the principle andscope of the invention as expressed in the following claims.

What is claimed is:
 1. A method of encoding a sequence of control data for storage on a medium, the control data to be used for subsequently reading information from the medium, comprising the steps of: (a) mapping, with a complementary rate (M/N) code, a block of M data bits of the sequence of control data into a block of N symbol bits, M being an integer greater than 1 and N being an integer greater than M, wherein any two adjacent symbol bits have no more than one transition in a row; and (b) storing the N symbol bits representing the control data on the medium.
 2. A method of generating a sequence of blocks of N symbol bits from a sequence of channel samples, the sequence of channel samples representing a sequence of control data and read from a medium, the method comprising the steps of: (a) receiving successive portions of the sequence of channel samples as transitions between sequential states of a trellis, wherein: the sequence of channel samples corresponds to the sequence of blocks of N symbol bits, each block of N symbol bits is formed from a block of M data bits of control data in accordance with a complementary rate (M/N) code, M being an integer greater than 1 and N being an integer greater than M, wherein any two adjacent symbol bits have no more than one transition in a row; (b) synchronizing a set of trellis phases and a set of forcing phases to the sequential states, the set of trellis phases corresponding to a block of N channel samples; and (c) determining, in accordance with a maximum-likelihood detection algorithm, a path through states of the set of trellis phases, the path of states corresponding to a received block of N symbol bits, wherein: for each trellis phase, a corresponding forcing phase provides, if necessary, a forced decision to the maximum-likelihood detection algorithm for a transition between states in the trellis, the forced decision based on a constraint of the rate (M/N) code.
 3. The method as recited in claim 2, further comprising the step e) mapping each block of N symbol bits into a block of M data bits to generate a sequence of control data, the control data to be used for subsequently reading additional information from the medium.
 4. A method of decoding a sequence of symbol bits generated from information read from a medium, the control data to be used for subsequently reading information from the medium, comprising the steps of: (a) receiving a sequence of blocks of N symbol bits detected from the medium, wherein each block of N symbol bits is formed by applying a complementary rate (M/N) code to a block of M data bits of control data, M being an integer greater than 1 and N being an integer greater than M, wherein any two adjacent symbol bits have no more than one transition in a row; (b) mapping each block of N symbol bits into a block of M data bits to generate the sequence of control data.
 5. An integrated circuit having an encoder that processes a sequence of control data for storage on a medium, the control data to be used for subsequently reading information from the medium, comprising: a register for storing a block of M bits of the sequence of control data; a logic circuit for mapping, with a complementary rate (M/N) code, the block of M data bits of the sequence of control data into a block of N symbol bits, M being an integer greater than 1 and N being an integer greater than M, wherein any two adjacent symbol bits have no more than one transition in a row, and wherein the N symbol bits representing the M data bits of the control data are stored on the medium.
 6. The invention as recited in claim 5, wherein the encoder is included in a magnetic recording system, the control data is servo data employed by a read head of the magnetic recording system to read information from the medium, and the encoder encodes the servo data for storage on the medium.
 7. An integrated circuit having a detector circuit for generating a sequence of blocks of N symbol bits from a sequence of channel samples, the sequence of channel samples representing a sequence of control data and read from a medium, the detector circuit comprising: a processor for implementing a trellis of a maximum-likelihood detection algorithm by receiving successive portions of the sequence of channel samples as transitions between sequential states of a trellis, the sequence of channel samples corresponding to the sequence of blocks of N symbol bits, each block of N symbol bits being formed from a block of M data bits of control data in accordance with a complementary rate (M/N) code, M being an integer greater than 1 and N being an integer greater than M, wherein any two adjacent symbol bits have no more than one transition in a row; and wherein the processor: (1) synchronizes a set of trellis phases to the sequential states, the set of trellis phases corresponding to a block of N channel samples, and (2) determines, in accordance with the maximum-likelihood detection algorithm, a path through states of the set of trellis phases, the path of states corresponding to a received block of N symbol bits; and a forcing logic circuit for generating a set of forcing phases synchronized to the set of trellis phases and to the sequential states, wherein for each trellis phase, a corresponding forcing phase of the forcing logic circuit provides the processor, if necessary, a forced decision to the maximum-likelihood detection algorithm for a transition between states in the trellis, the forced decision based on a constraint of the rate (M/N) code.
 8. The invention as recited in claim 7, further comprising a logic circuit that maps each block of N symbol bits into a block of M data bits to generate a sequence of control data, the control data used subsequently for reading additional information from the medium.
 9. The invention as recited in claim 7, wherein the detector circuit is included in a magnetic-recording system, the control data is servo data employed by a read head of the magnetic recording system to read information from the medium, and the encoder encodes the servo data for storage on the medium.
 10. The invention as recited in claim 7, wherein the detector circuit is employs a maximum-likelihood algorithm accounting for a partial response of a recording channel of a magnetic medium, the magnetic medium being the medium from which the sequence of channel samples is received.
 11. An integrated circuit having a decoder for decoding a sequence of symbol bits generated from information read from a medium, the control data used subsequently for reading information from the medium, comprising: a register for storing a sequence of blocks of N symbol bits detected from the medium; and a logic circuit for mapping each block of N symbol bits into a block of M data bits to generate the sequence of control data, wherein each block of N symbol bits is formed by applying a complementary rate (M/N) code to a block of M data bits of control data, M being an integer greater than 1 and N being an integer greater than M, wherein any two adjacent symbol bits have no more than one transition in a row.
 12. The invention as recited in claim 11, wherein the decoder is included in a magnetic recording system, the control data is servo data employed by a read head of the magnetic recording system to read information from the medium, and the encoder encodes the servo data for storage on the medium.
 13. A computer-readable medium having stored thereon a plurality of instructions, the plurality of instructions including instructions which, when executed by a processor, cause the processor to implement a method of encoding a sequence of control data for storage on a medium, the control data to be used for subsequently reading information from the medium, the method comprising the steps of: (a) mapping, with a complementary rate (M/N) code, a block of M data bits of the sequence of control data into a block of N symbol bits, M being an integer greater than 1 and N being an integer greater than M, wherein any two adjacent symbol bits have no more than one transition in a row; and (b) storing the N symbol bits on the medium.
 14. A computer-readable medium having stored thereon a plurality of instructions, the plurality of instructions including instructions which, when executed by a processor, cause the processor to implement a method of generating a sequence of blocks of N symbol bits from a sequence of channel samples representing information and read from a medium, the method comprising the steps of: (a) receiving successive portions of the sequence of channel samples as transitions between sequential states of a trellis, wherein: the sequence of channel samples corresponds to the sequence of blocks of N symbol bits, each block of N symbol bits is formed from a block of M data bits of control data in accordance with a complementary rate (M/N) code, M being an integer greater than 1 and N being an integer greater than M, wherein any two adjacent symbol bits have no more than one transition in a row; (b) synchronizing a set of trellis phases and a set of forcing phases to the sequential states, the set of trellis phases corresponding to a block of N channel samples; and (c) determining, in accordance with a maximum-likelihood detection algorithm, a path through states of the set of trellis phases, the path of states corresponding to a received block of N symbol bits, wherein: for each trellis phase, a corresponding forcing phase provides, if necessary, a forced decision to the maximum-likelihood detection algorithm for a transition between states in the trellis, the forced decision based on a constraint of the rate (M/N) code.
 15. The computer-readable medium as recited in claim 14, further comprising the step e) mapping each block of N symbol bits into a block of M data bits to generate a sequence of control data, the control data to be used for subsequently reading additional information from the medium.
 16. A computer-readable medium having stored thereon a plurality of instructions, the plurality of instructions including instructions which, when executed by a processor, cause the processor to implement a method of decoding a sequence of symbol bits generated from information read from a medium, the control data to be used for subsequently reading information from the medium, the method comprising the steps of: (a) receiving a sequence of blocks of N symbol bits detected from the medium, wherein each block of N symbol bits is formed by applying a rate (M/N) code to a block of M data bits of control data, M being an integer greater than 1 and N being an integer greater than M, wherein any two adjacent symbol bits have no more than one transition in a row; (b) mapping each block of N symbol bits into a block of M data bits to generate the sequence of control data.
 17. An encoder for processing a sequence of control data for storage on a medium, the control data to be used for subsequently reading information from the medium, comprising: storage means for storing a block of M data bits of the sequence of control data; mapping means for mapping, with a complementary rate (M/N) code, the block of M data bits of the sequence of control data into a block of N symbol bits, M being an integer greater than 1 and N being an integer greater than M, wherein any two adjacent symbol bits have no more than one transition in a row, and wherein the N symbol bits representing the control data are stored on the medium.
 18. A detector circuit for generating a sequence of blocks of N symbol bits from a sequence of channel samples, the sequence of channel samples representing a sequence of control data and read from a medium, the detector circuit comprising: a processor for implementing a trellis of a maximum-likelihood detection algorithm by receiving successive portions of the sequence of channel samples as transitions between sequential states of a trellis, the sequence of channel samples corresponding to the sequence of blocks of N symbol bits, each block of N symbol bits being formed from a block of M data bits of control data in accordance with a rate (M/N) code, M being an integer greater than 1 and N being an integer greater than M, wherein any two adjacent symbol bits have no more than one transition in a row; and wherein the processor: (1) synchronizes a set of trellis phases to the sequential states, the set of trellis phases corresponding to a block of N channel samples, and (2) determines, in accordance with the maximum-likelihood detection algorithm, a path through states of the set of trellis phases, the path of states corresponding to a received block of N symbol bits; and a forcing logic circuit for generating a set of forcing phases synchronized to the set of trellis phases and to the sequential states, wherein: for each trellis phase, a corresponding forcing phase of the forcing logic circuit provides the processor, if necessary, a forced decision to the maximum-likelihood detection algorithm for a transition between states in the trellis, the forced decision based on a constraint of the rate (M/N) code.
 19. The invention as recited in claim 18, further comprising mapping means for mapping each block of N symbol bits into a block of M data bits to generate a sequence of control data, the control data to be used for subsequently reading additional information from the medium.
 20. A decoder circuit for decoding a sequence of symbol bits generated from information read from a medium, the control data to be used for subsequently reading information from the medium, comprising: storage means for storing a sequence of blocks of N symbol bits detected from the medium; and mapping means for mapping each block of N symbol bits into a block of M data bits to generate the sequence of control data, wherein each block of N symbol bits is formed by applying a complementary rate (M/N) code to a block of M data bits of control data, M being an integer greater than 1 and N being an integer greater than M, wherein any two adjacent symbol bits have no more than one transition in a row. 